Multipolar theory of blackbody radiation shift of atomic energy levels and its implications for optical lattice clocks

TLDR

The characteristic blackbody radiation wavelength is comparable to the fine‑structure intervals of the $^{3}P$ state in these optical‑lattice clocks. The study aims to evaluate blackbody radiation shifts of the $^{3}P_{0}\!-\!^{1}S_{0}$ clock transition in Mg, Ca, Sr, and Yb and to develop a multipolar theory to assess M1 and E2 contributions. Using accurate relativistic many‑body calculations, the authors compute dominant electric‑dipole BBR shifts and formulate a multipolar framework to evaluate magnetic‑dipole and electric‑quadrupole contributions. At room temperature, uncertainties in the electric‑dipole BBR shifts are large enough to jeopardize the targeted $10^{-18}$ fractional accuracy, and although multipolar corrections are necessary for that goal, they are presently obscured by the dominant uncertainties.

Abstract

Blackbody radiation (BBR) shifts of the $^{3}P_{0}\text{\ensuremath{-}}^{1}S_{0}$ clock transition in the divalent atoms Mg, Ca, Sr, and Yb are evaluated. The dominant electric-dipole contributions are computed using accurate relativistic many-body techniques of atomic structure. At room temperatures, the resulting uncertainties in the $E1$ BBR shifts are large and substantially affect the projected ${10}^{\ensuremath{-}18}$ fractional accuracy of the optical-lattice-based clocks. A peculiarity of these clocks is that the characteristic BBR wavelength is comparable to the $^{3}P$ fine-structure intervals. To evaluate relevant $M1$ and $E2$ contributions, a theory of multipolar BBR shifts is developed. The resulting corrections, although presently masked by the uncertainties in the $E1$ contribution, are required at the ${10}^{\ensuremath{-}18}$ accuracy goal.